[tex]\large\mathfrak{{\pmb{\underline{\orange{Given }}{\orange{:}}}}}[/tex]
[tex]2x - 40y = 73...(i)[/tex]
[tex]7x + 65y = 332...(ii)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\pink{To\:find }}{\pink{:}}}}}[/tex]
The values of [tex]x[/tex] and [tex]y[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\green{Solution }}{\green{:}}}}}[/tex]
[tex]x=43.96 [/tex] and [tex]y = 0.373 [/tex].
[tex]\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}[/tex]
Let us solve this by substitution method.
From [tex]eqn.\:(i),\:we\:have [/tex]
↬[tex]2x - 40y = 73[/tex]
↬[tex]2x = 73 + 40y[/tex]
↬[tex]x = \frac{73 + 40y}{2}...(iii) \\ [/tex]
Substituting the value of [tex]x[/tex] in [tex]eqn.\:(ii)[/tex] gives us
↬[tex]7( \frac{73 + 40y}{2} ) + 65y = 332 \\ [/tex]
↬[tex] \frac{511 + 280y}{2} + \frac{65y \times 2}{1 \times 2} = 332 \\ [/tex]
↬[tex] \frac{511 + 280y + 130y}{2} = 332 \\ [/tex]
↬[tex]410y + 511 = 332 \times 2[/tex]
↬[tex]410y = 664 - 511[/tex]
↬[tex]y = \frac{153}{410} \\ [/tex]
↬[tex]y = 0.373[/tex]
Now, plug the value of [tex]y[/tex] in [tex]eqn.\:(i)[/tex]
↬[tex]2x - 40 \times 0.373 = 73 \\ [/tex]
↬[tex]2x - 14.92= 73 [/tex]
↬[tex]2x = 73 +14.92[/tex]
↬[tex]x = \frac{87.92}{2} \\ [/tex]
↬[tex]x = 43 .96[/tex]
Therefore, the values of [tex]x[/tex] and [tex]y[/tex] are [tex]\boxed{ 43.96 }[/tex] and [tex]\boxed{ 0.373 }[/tex] respectively.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
